Langmuir 1993,9, 2844-2850
2844
Lamellar to Vesicle Transitions of Highly Charged Bilayers E. Z. Radlihska,*9+T. N. Zemb,t J.-P. Dalbiez,t and B. W. Ninhamt Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia, and Service de Chimie Mol&culaire,Centre d'Etudes de Saclay, Bbt 125, 91191 Gif sur Yvette, France Received March 25,1993. In Final Form: August 6,1993@ We study the phase diagram of the binary didodecyldimethylammoniumacetatelwater system from 4.4 x 10-6to 0.1volume fractionof surfactantusing classicaland dynamiclight scattering,SANS,and electrical conductivity measurements. A thermodynamicallystable dilute vesicular phase exists at concentrations below 0.006 surfactant volume fraction. With increased concentrationof surfactant a symmetric sponge (L3)phase and lamellar phase are observed separated by a two-phaseregion. The symmetricspongephase exists in the concentration region from 5 X 1V to 2.6 X 1W2volume fraction. 1. Introduction
The structure of amphiphilic systems containing fluctuating films or membranes has been the subject of extensive experimentall-lO and theoretical investig a t i o n ~ . ~In~ such - ~ ~ systems, the competition between the molecular (van der Waals interaction, hydration repulsion, screened electrostatic interacti~n)'~ and fluctuation-induced interactions15J6may result in a variety of phases. For a dilute amphiphilic system (i.e. when the persistence length of the structure is large compared to the membrane thickness) the thermodynamics of phases formed may be described by the statistical physics of surfaces embedded in three-dimensional space.12 On the other hand, it has been d e m o n ~ t r a t e d ' ~that - ~ ~the phase equilibria in surfactant systems can be well interpreted using a geometricalapproach. On this geometricalmodel, surfactant molecules are characterized by an effective surfactant parameterl'p = v/al (v is the molecular volume, 1 is the molecular length, and a is the polar group crosst Australian National University. t Centre #Etudes de Saclay.
Abstract published in Advance ACS Abstracts, October 1,1993.
(1) Porte, 6.;Appell, J.; Bassereau, P.; Marignan, J. J. Phys. (Paris) 1989,50, 1335. (2) Gazeau, D.; Bellocq, A. M.; Row, D.; Zemb, T.Prog. ColloidPolym. Sci. 1989, 79, 226. (3) Fontell, K. In Colloidal Dispersions and Micellar Behaviour, ACS Symposium Series S; American Chemical Society Washington, DC, 1975; D 270. (4) Lang, J. C.; Morgan, R. D. J. Chem. Phys. 1980, 73, 5849. (5) Mitchell, D. J.; Tiddy, G.J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79,975. (6) Benton, W. J.; Miller, C. A. J. Chem. Phys. 1983,87,4981. (7) Nilsson, P.-G.; Lindman, B. J. Phys. Chem. 1984,88,4764.
(8)Marignan, J.; Appell, J.; Bassereau, P.; Porte, G.;May, R. P. J. Phys. (Paris) 1989,50,3553. (9) Roux,D.; Cates, M. E.; Olsson, U.; Ball, R.C.; Nallet, F.; Bellocq, A. M. Europhys. Lett. 1990, 11, 229. (10)Strey,R.;Schomacker,R.;Row,D.;Nallet,F.;Olsson,U. J.Chem. Soc., Faraday Trans. 1990,86, 2253. (11) Leibler, S.; Lipowsky, R.;Peliti, L. In Physics of Amphiphilic Layers; Meunier, J., Langevin, D., Boccara, N., Eds.; Springer-Verlag: Berlin, 1987; p 74. (12) Huse, D. A.; Leibler, S. J.Phys. (Paris) 1988,49,605. (13) Roux, D.; Cates, M. E. In Dynamics and Paterns in Complex Fluids; Onuki, A,, Kawasaki, K., Eds.; Springer-Verlag: Berlin, 1990; p 19. (14) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1985. (15) Helfrich, W. 2.Naturforsch. 1973, Bc, 693. (16) Helfrich, W. 2.Naturforsch. 1978,33a, 305. (17) Israelachvili, J. N.; Mitchell, J. D.; Ninham, B. W. J . Chem. SOC., Faraday Trans. 2 1976, 72, 1525. (18) Anderson, D.; Wennerstrsm, H.; Oleson, U. J. Phys. Chem. 1989, 93, 4243. (19) Hyde, S. T. Colloq. Phys. C7 1990,23, 209. (20) Hyde, S. T. Prog. Colloid Polym. Sci. 1990,82, 236.
sectionalarea). The surfactant parameter canbe exprmed in terms of interfacial curvatures and vice v e r ~ a . It ~~*~ has been shown that fluid uncharged surfactant membranes are characterized by low surface tension and small membrane bending rigidity, k,.21122 Consequently, the membranesare subject to strong oubof-planeundulations. It has been shown recently that for the values of k, of the order of the thermal energy, kBT, the thermally induced interaction dominates at large distances provided the electrostaticinteractions are either absent or screened.%% However,the presence of electricalcharges of high density may suppress the undulation-related force as demonstrated for the SDS/pentanoVwater Three different theoretical evaluations of the electrostatic part of the bending energyhave been given in the literat~re,2'-~ giving estimates of about lOkBT for the bending constant of the bilayer if the area per unit charge is assumed to be 0.7nm2. Moreover,it was recently predicted theoretically that long range electrostatic interactions significantly affect the value of bending constant of membra11e.2~ Our aim in this study is to investigate phase behavior of a diluted assembly of planar membranes, and a simple binary surfactant/water system was chosen. A doublechain quaternary ammonium salt was used, didodecyldimethylammonium acetate (DDAA). These surfactantsare insolublein water and their aggregationproperties have been found to be strongly dependent on the counterion, thus demonstrating the importance of the longrange electrostatic interaction for the phase equilibria (see refs 30 and 31). The selection of a dilute binary system enables us to neglect the van der Waals and hydration forces and concentrate on the interplay between the electrostatic and entropy-induced interactions. To give an example, the DDA bromide salt/water system forms a highly swollen smectic lamellar phase above 3 7% (w/w) of surfactant. At higher water dilution (below 0.15% (w/w) (21) de Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982,86, 2294. (22) Brochard, F.; de Gennes, P. G.;Pfeuty, P. J. Phys. (Paris) 1976, 37, 1099. (23) Pincus, P.; Joanny, J.-F.; Andelman, D.Europhys. Lett. 1990,11, 762. .
(24) Larche, F. C.; Appell, J.; Porte, G.;Bassereau, P.; Marignan, J. Phys. Rev. Lett. 1986,56, 1700. (25) Roux, D.; Safiiya, C. R.J. Phys. (Paria) 1988,49, 307. (26) Safiiya, C. R.;Roux, D.; Smith, G.S.; Sinha, S. K.; Dimon, P.; Clark, N. A.; Bellocq, A. M. Phys. Rev. Lett. 1986,57, 2718. (27) Mitchell, D. J.; Ninham, B. W. Langmuir 1989,5,1121. (28) Lekkerkerker, W. N. H. Physica A 1989,159, 319. (29) Fogden, A.; Mitchell, D. J.; Ninham, B. W. Langmuir 1990,6,169. (30)Radlideka, E. Z.; Ninham, B. W.; Dalbiez, J.-P.; Zemb, T. N. Colloids Surf. 1990, 46, 213. (31) Dubois, M.; Zemb, T. N. Langmuir 1991, 7, 1352.
0743-746319312409-2844$04.00/0 0 1993 American Chemical Society
Langmuir, Vol. 9, No. 11, 1993 2846
Lamellar to Vesicle Transitions
of surfactant) a dilute vesicle phase is observed. The transition between these two phases is strongly first order. At intermediate concentrations of surfactant there is a metastable asymmetric sponge phase which has been evidenced by a broad scattering peak whose position is independent of concentration. This metastable structure transforms to the ordered lamellar phase after more than 30 days of e q ~ i l i b r a t i o n . ~ ~
60 1-1
Asymm
2. Experimental Section 2.1. Materials. Didodecyldimethylammonium bromide (DDAB) was obtained from Sogo Pharmaceutical Co. and ion exchanged to the hydroxide form using Amberlite IRA-400 OH resins obtained from Sigma Co. Details of the preparation procedure are given in ref 32. The didodecyldimethylammonium acetate (DDAA) was made from hydroxide salt by titration with acetic acid. The elementalanaly~isindicatedno traces of bromine and a low degree hydration of the powder. The samples were prepared by weight in doubly distilled water under dust free conditions in a Laminar flow cabinet. All solutions used for light scattering measurements were filtered through a 0.22-pm Millipore filter into the light scattering cell and centrifuged before measurements. 2.2. Light Scattering. A detailed description of the measuring system and associated experimental procedures is given in ref 33-35. The light source was an Ar+ h e r with a wavelength of 514.5 nm and power within the range 100-1OoO mW. The incident light was verticallypolarized and focused on the sample. The sample was contained in a cylindrical test tube of 25 min diameter, placed in a bath filled with toluene in order to match the refractive index of scattering cell. Measurementswere carried out using a goniometer type AMTEC SM 200 in the range of scattering angles 0 between 10" and 160". The angular resolution of the optical system varied from 1.0 X 10-3to 26 X 10-3rad. This resulted in the relative resolution of the scattering wavevector, AQ/Q, varying from less than 0.01 for scattering angles larger than 40" to about 0.04 for Q = 10". During the measurements the sample temperature was maintained at 25 0.1 "C. For a few concentrations the light scattering was measured at temperatures of 35 0.1 and 40 & 0.1 "C. The instrument was calibrated using scattering from pure benzene and pure water specimens. The scattered light was collected through a system of slits, which defiies the scattering volume. The intensity was recorded with a photomultiplier (EM19863 KB 100) followed by a 64-channel digital correlator (Malvem Model K 7025). Dynamic light scattering measurements were performed at a Tied angle of 90°. The scattered light was observed by homodyne detection. The output signal from the photomultiplier was amplified and processed by a discriminator followed by the digital correlator. The autocorrelation function was computed in the multibit mode and analyzed using the method of ~ u m u l a n t s . ~ 2.3. Small Angle Neutron Scattering. Small angle neutron scattering (SANS) experiments, were carried out at the PACE facility at Orphbe (Saclay,France). Samples were prepared with D20 instead of water. Contrast for the DDAA/D20 solutions used in experiments was calculated to be Ap = 6.56 X 1O1O using known values of coherent scattering lengths and the volumes of chemical groups?' Experimental data were corrected using standard methods, includingabsolute scalingby comparisonwith scattering of pure D20.as,39Scattered intensities corresponding to overlapping angular ranges were collected for each sample for
*
*
(32)Ninham, B. W.; Evans, D. F.; Wel, G. J. J. Phys. Chem. 1983,87, 5020. (33)Drifford, M.; Belloni, L.; Dalbiez, J.-P.; Chattopadhyay, A. K. J. Colloid Interface Sci. 1985,105, 587. (34)Drifford, M.; Dalbiez, J.-P. J. Phys. Chem. 1984,88, 5368. (35)Tivant, P.; Turq, P.; Drifford, M.; Magdelenat, H.; Menez, R. Biopolymers 1983,22, 643. (36)Cummins, H.Z.;Pusey, P. N. InPhoton CorrelationSpectroscopy and Velocimetry;Cummins, H. Z., Pike, E. R., Eds.; Plenum Press: New York, 1977;p 164. (37)Cabane, B. In Surfactant Solutions, New Methods of Inuestigation; h a , R., Ed.; Marcel Dekker: New York, 1987;p 57. (38)Zemb, T. N. In French CEA Report R-5301,1985. (39)Cabane, B.; Duplessix, R.; Zemb, T. J. Phys. (Paris) 1985, 46, 2161.
I
,
1-1
I
,
10'' SURFACTANT VOLUME FRACTION
Figure 1. Phase diagram of DDAA water system: asymmetric sponge,symmetric sponge,and lamellar phase regions are shown. the following intervals of the scattering vector Q (A-l): 0.0027 < Q < 0.052, 0.0075 < Q < 0.14, and 0.011 < Q < 0.58.
3. Results and Discussion 3.1. PhaseDiagram. The experimental phasediagram was first examined by visual observation of the sample8 in a thermostated water bath in transmitted light and between crossed polarizers. The observations were carried out after equilibrating samples for a few days and again after 3 months. In the case of didodecyldimethylammonium acetate (DDAA) the isotropic, transparent phase is obtained for surfactant volume fractions from 4.4 X 10-6 to 2.5 X 1k2.This phase is identified as the L3 phase (disordered connected phase, sponge phase) formed by surfactant bilayers in water. It is demonstrated that for the surfactant volume fraction about 5 X 103this phase undergoes a (second order) transition from asymmetricto the symmetric spongestate as the surfactant concentration increases. This new kind of phase transition was first postulated t h e o r e t i ~ a l l y 'and ~ ~ ~then ~ observed experimentally in a quaternary systemg and a pseudotemary system.41 According to theory, spontaneous breaking of inside/ outside (I/O) symmetry either may occur as a first-order transition (i.e. from a sponge phase to small vesicle^^*^ or may be of second order, in which case Ising-like thermodynamic singularities should be ~ b s e r v e d . ' ~Breaking ~~~ of the L3 phase into smaller structures was postulated on the basis of conductivity data for a binary nonionic surfactant-water system.1° Because of the extreme dilution, however, the exact topology of the phase diagram in the low surfactant concentration region cannot be determinedwith precision by visual observation only. The region between & = 4.4 X 10-6 and $B = 2.5 X 1k2is monophasic. Samples are transparent. When examined between crossed polarizers the samples of concentrations in the region 0.025 I & I 0.10 are flow birefringent. The sample of surfactant volume fraction 0.10 is birefringent and opaque. Samples of surfactant volume fractions between 5 X lk3and 2.5 X 1k2show some intemal turbidity but the concentration is too low to notice flow birefringence. 3.2. Classical and Dynamic Light Scattering. The classical light scattering studies were carried out in the range of concentrations from 4.4 X 10-6 to 0.05 volume fraction of surfactant. In contrast to the DDAOH/water system,3O the diluted suspensions of DDAA exhibit flow birefringence which is a feature characteristic of the disordered connected phase, La. The existence of meta(40)Cates, M. E.; h u x , D.; Andelman, D.; Milner, S. T.; Safran, S.A. Euro-phys. Lett. 1988, 5 , 733. (41)Codon, C.; RQux, D.; Bellocq, A. M. Phys. Rev. Lett. 1991, 66, 1709.
Radlifiska et al.
2046 Langmuir, Vol. 9,No.11, 1993
stable sponge phase in DDAB and DHDAA was demonstrated via studies over a wide range of surfactant c~ncentration.~~ The density correlation functions in the vicinity of the symmetric/asymmetricphase transformation within the sponge phase region were calculated in the Landau-Ginzburg approximation using a perturbation a p p r ~ a c h . ' ~ ~ ~ ~ ~ ~ ~ ~ ~ In these calculations, the symmetry of the sponge phase is described using two order parameters. One is the classical Landau-Ginzburg order parameter, which chang- 8 ~ " ' " ' ' \ I ! es continuously from a nonzero value in the asymmetric 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 sponge to zero value in the symmetric sponge (vesicle) Q X 103(A1) and is given by t = $ - 1/2, where $ = VinsiddVtotal and V h i d e + Voutside = Vba. The second order parameter is Figure 2. Intensityof the scatteredlight versus scatteringvector selected in such a way that it is equal zero at the transition for the sample of surfactant volume fraction 4.4 X W. Solid circles represent experimentalpoints. Dotted and broken lines point and nonzero on both sides of the transition. This correspondto bimodal scatteringby vesicles and were calculated parameter is defined as the deviation of the surfactant accordingto ref 45. The following parameters were wed: ml = volume fraction from its critical value at the transition 1.33, m2 = 1.44, n = 1.33, bilayer thickness d = 29 A, and b l = point: p = 4 - &itid. The symmetric/asymmetric@/A) lOOOA, b2 = 2300A. Thetheoreticalfitoftotalecatteringintensity symmetry is of Ising-like character and it was shown41 is shown with a solid line. that it can break spontaneously. A simplified form of the Table I. Effective Diffusion Coefficients D.n and the static structure factor is given by Coulon et al.41 Since the Radii of Vesicles Calculated from Quasi-ElasticLight numerical difference between the full and simplified Scattering for Q = 1.7 x 104 A formula is not detectable in the experiment, we use the latter. In this form, the light scattering intensity for the symmetric sponge phase can be expressed as 4.4 x 1o-e 2.4 & 0.1 850 1.3 X 1 0 6 3.1 X 1 0 6 4.4 x 1 0 6
whereas for the asymmetric sponge phase it is
2.2 x lo-' 4.4 x lo-'
2.9 h 0.3 3.2 h 0.3 2.7 & 0.2 1.8 0.8 2.0 & 0.8
860 716 1160
790 1065
sponge phase is about 140 A. The character of this phase transition could be best determined by analyzing the concentration dependenceof correlation length [,,for the fluctuations of the order parameter 7. However, the In the above equations rp= l/a and r, = 1/A are the correlation lengths in our system were typically of the susceptibilitiesfor p and 7, respectively, whereas &, ( ~ / a ) ' / ~ order of 10 OOO A or larger and could not be determined and& = (C/A)1/2are the correspondingcorrelation lengths. since the shapes of scattering curves (eqs 1 and 2) become Quantities K and K' are proportional to the square of the insensitive to the correlation length in the regime &, >> b. coupling constant X between the order parameters. For the same reason, the expected divergence of the total scattered intensity has not been observed. The light scattering data obtained in the surfactant volume fraction region 4.4 X 10-6 to 2.5 X were fitted The above discussion is illustrated using data for two assuming scattering from the sponge phase. Experimental volume fractions close to the A/S phase transition. In data for high dilution (up to & = 0.0022) were fitted using Figure 3, light scattering results for & = 0.0022 are eq 2. We note that at high water content an equally good presented. It is clear that these data can be only fitted fit could be obtained by using a bimodal distribution of by formula 2 (asymmetric sponge), but the experimental vesicles of radii 1OOO and 2300 A, similar to the case of scatter is large and we can only determine that the DDAOH.30 An example for surfactant volume fraction of correlation length is larger than 10 OOO A. On the other 4.4 X 10-6 is shown in Figure 2. From the dynamic light hand, for dS= 0.005 (Figure 4) the light scattering data scattering measurements the values of Deffand the radii can be only fitted using formula 1 (symmetric sponge), of the scattering objecta were caldatad using the cumulant but it can only be estimated that the correlation length method extrapolated to 7- = O.u Results are given in is no less than 16 OOO A. Table I. In the DDAA concentration range from 4.4 X The illustrative way of discriminating between the two 10-6 to 4.4 X 1W of surfactant volume fraction, the different phases, symmetric and asymmetric, is to plot correlation decays were exponential, which indicates data as 1/1(Q)versus Q2. This is shown in Figure 5 for two unimodal size distribution. The effective diffusion coefvolume fractions of surfactant: & = 4.4 X lP (A) and Cbs ficients are similar to these found for vesicles in DDAOH.30 = 0.025 (SI. The two curves are clearly of opposite Data obtained for samples of higher surfactant concencurvatures. The correlation lengths for our samples are trations (0.005 C I 0.025) could be only fitted using the compiled in Table 11. correlation function for the symmetricsponge phase given 3.3. Electrical Conductivity. The experimental by eq 1. The density correlation length tpwas assumed values for DDAA at 25 "C have been reduced by dividing to be much smaller than Ell. tPis of the order of the typical them by the conductivity values measured for water radii of curvature,l2I2lwhich is about 1OOO A in the solutions of sodium acetate corresponding to the same asymmetricsponge phase. On the other hand the density concentration of acetate ions. The obtained relative correlation length as measured by SANS for symmetric conductivity of water solution of DDAA versus surfactant volume fraction is shown in Figure 6. (42) Roux, D.; Coulon,C.;Cabs, M.E . J. Phys. Chem. 1992,96,4174. Because we study a strictly binary surfactant/water (43) Granek, R.; Cabs, M. E . Phys. Reu. A 1992,46,3319. system (in contrast to surfactant/salt/water systems) the (44) Pusey, P. N. J.Phys. A 1975,8,1433. (45) Kerker, M. The Scattering of Light;Loebl: New York, 1969. electrically active chemical impurities unintentionally n
V'TI 11
2
Langmuir, Vol. 9, No.11, 1993 2847
Lamellar to Vesicle Transitions
20
I
4
It Qg=0.0022
5
1 1
c ? 0
Y
0.002 Q
.
1.0 -
g . \
7
0.8 -
0.6 -
-
0.4
0 0.001
1.2
0.2 -
0.003
(A’ 1
Figure 3. Classical light scattering intensity distribution for the sample of surfactant volume fraction 0.0022. The l i e s represent best fits to the symmetric function (eq 11, line S = 10 OOO A), and two of the possible fits to the asymmetricfunction (eq 2), lines A1 and Az. The corresponding correlation lengths are 60 OOO A (AI) and 10 OOO (Ad.
(e,,
0
1
2
3
4
5
6
7
d (k) x 106 Figure 5. Inverse of the scattered intensity versus Qz. Data correspondto the following volume fractions of surfactant: open squares, 0.025; f i e d squares, 4.4 X 10-8. Solid linea represent the best fit to formulas for asymmetric sponge phase (A, En = 2300 A) and symmetric sponge phase (S,E,, = 10 OOO A). 1.Or
0.0
0
0.001
0.001
0.002
0.003
Q (A-’)
Figure 4. Classical light scattering intensity distribution for the sample of surfactant volume fraction 0.006. The lines represent best fits to the asymmetric function (eq 2), line A (Eq = 16 OOOA),andtwoofthepossiblefitatothesymmetricfunction
(eq I), lines SIand SZ. The corresponding correlation lengths are 60 OOO A (SI)and 16 OOO A (SZ).
(46)JBnsson, B.;WennerstrBm, H.;Nilsson, P.G.; Linse, P.Colloid Polym. Sci. 1986, 264,77. (47) Lindman, B.;Brun, B. J . Colloid Interface Sci. 1973,42, 388.
0.1
F’igure 6. Relativespecific conductivityvmun surfactantvolume fractionat the temperatureof 25 OC. Arrow indicatesthe position of asymmetric to symmetric sponge phase transition. Table 11. Cormlation Lengths Obtained by Fitting the Classical Light Scattering Data for Samplea of Diffemnt Surfactant Volume Fraction @nul
introduced during the surfactantpreparation process may contribute to the absolute value of conductivity. However, the shape of the relative conductivity curve versus concentration should remain unchanged. There are two distinct regions present in the relative conductivity plot: rapid decrease for the volume fraction of surfactant less than about 0.002 and very slowlychangingvalues for larger values of volume fraction (Figure 6). In the small volume fractionregion DDAA formsvesicles. With the obstruction effect caused by the presence of electrically neutral spherical particles,4Bthe relative mobility of ions should slowly decrease from its initial value of 1with the increased surfactant volume fraction. For instance, this kind of behavior has been observed in micellar systems.47 However, for large, strongly oblate objecta the decrease of relative conductivity is limited to a much narrower region
0.01
SURFACTANT VOLUME FRACTION
4.4 x 1v 1.3 X 10-6 2.2 x 10-6
Ell
(A)
2300 3250 5ooo
@nur 2.2 x 1o-a 5.0 X 10-8 2.5 X lVz
E? (A) >loo00 >16Ooo loo00
of surfactant volume fraction. Since the mobilities of sodium ions and acetate counterions are roughly the same (5.19 X 104 and 4.23 X 104 cm2V-I respectively), a limiting value of 0.33 (l/2 X 2/3) is expected for DDAA on theoretical groundsa assuming that all the acetate counterions take part in the electric transport. The discrepancy between the measured (about 0.55) and expected (0.33) value may be caused by the impurity effecta. Topology of the asymmetricsponge phase evolves upon increase in surfactant concentration. The domains of the minority componentpercolate before the volume fraction occupied by them (i.e. the “inside” region in the present case), $, reaches 0.5.12 For the symmetric sponge phase (48)A d a ” , A. W . A. Textbook of Physical Chemistry; Academic Press: New York, 1979; p 446.
Radlihska et al.
2848 Langmuir, Vol. 9, No. 11, 1993
-2
.
*..a.
1
-2.5
.
I
-2.0
.
I
.
-1.5
I
-1.0
.
0I
-0.5
WQ)
DDAB
10
io4
10"
io-*
io-'
SURFACTANT VOLUME FRACTION
Figure 7. Double logarithmic plot of the equivalent conductance versus surfactant volume fraction for DDAB/water and DDAA/ water systems at the temperature of 25 OC. Data for NaAc are shown for comparison. -2 -l P
' elw
0
I
I
L -2.5
-2.0
-1.5
-1.0
-0.5
WQ)
Figure 9. Double logarithmic plot of SANS intensity (cm-l) versus scattering vector Q. Data correspond to the following volume fractions of surfactant: (top) squares, 0.05; diamonds, 0.025;triangles, 0.015;(bottom) inverted triangles, 0.004;circles, 0.001.
' A A
A
g io*-: a z
A~~
A::
Table 111. Calculated and Experimental Invariant and Specific Surface for the Samples Measured in SANS
8 z
3
9.
5
3
101'
io4
io-'
io-'
I
SURFACTANT VOLUME FRACTION
Figure 8. Double logarithmic plot of the equivalent conductance versus surfactant volume fraction at temperatures (filledsquares)
10 O C , (open squares) 25 "C,(filled triangles) 40 O C , and (open triangles) 60 "C.
the evolution of coniinuous disordered lamellar structure is responsible for the gradual mobility decrease owing to increasingtortuosity of ion paths.I8 For surfactant volume fractions larger than 0.025,the system becomes a twophase spontaneous emulsion (L3+ La)and the value of conductivity stabilizes. The equivalent conductivity for typical strong electrolytes decreases with increasing concentration. The deviation from decrease proportional to c1I2is the result of long range Coulomb interactions between ions. In the surfactant/water systems, one expects much stronger manifestation of the ion scattering effects by the large aggregates. The equivalent conductivities versus surfactant volume fraction for the two corresponding didodecyldimethylammonium salts together with the equivalent conductivity of sodium acetate are shown in Figure 7. The role of scattering effects, which depend on the microstructure within different surfactant/water system, is clearly visible. The influence of temperature on the concentration dependence of equivalent conductivity of DDAA was measured for four temperatures in the range 10 to 60 OC. Evidently, the microstructure is not temperature sensitive in this range as presented in Figure 8; this is a direct verification that k, >> kBT. 3.4. Small Angle Neutron Scattering. SANS experiments were performed on the samples of the volume fraction of surfactant 0.001,0.004,0.015,0.025,0.05, and 0.10 in D2O. The values of invariant and specific surface calculated for measured spectra and from the composition
0.05 0.025 0.015 0.004 0.001
(cm4) Q * ~(cm-9 J 4.03 X lpl 3.06 X lpl 2.07 X lpl 1.81 X lpl 1.25 X loz1 1.00X lpl 3.38 X 1020 2.92 X lom 8.49 X lOle 9.39 X 10IB
Q*cllcd
Ccllcd (cm-9
4.0 X 106 2.0 X 1@ 1.2 X 1@ 3.2 X 10' 8.0 X 109
(cm-9 10.7 X l@ 9.3 X 106 2.04 X 106 3.21 X 10' 5.85 X 1Oa
L t l
of the samples are shown in Table 111. The first four samples were pure sponge phase as evidenced by light scattering data, conductivity measurements, and visual observation. In the view of the light scattering results the system undergoes a phase transformation from an asymmetric sponge phase to symmetric state at some value of surfactant volume fraction between qh = 0.0022 and & = 0.005. The samples of the surfactant volume fraction of 0.05 and 0.10 are in the two-phase region (L3+ La).The f i s t one is mainly sponge phase (asshown by light scattering), the second is mainly lamellar phase. The data for the samples of surfactant volume fraction 0.05,0.025, and 0.015 have a character typical for the L3 phase: a broad maximum followed by a long decaying tail at large values of When the scattering intensity is normalized for the surfactant volume fraction (see Figure 9, top), the spectra coincide in the region of large Q, m expected for the sponge p h a ~ e The . ~ ~data ~ ~for samples of surfactant volume fractions 0.004 and 0.001 exhibit a different character: spectra coincide when drawn in normalized form (see Figure 9, bottom). From the light scattering results it is known that the sample of surfactant volume fraction 0.001 is in the asymmetricsponge phase region. SANS intensity curves together with the light scattering data for the samples with surfactant volume fractions 0.05, 0.025, and 0.015 are shown in Figures 10-12. The initial slope of -2, characteristic of two-dimensionalobjects, decreases to the value of -4 in the Porod region, indicating a smooth, wellQ.118949
(49) Skouri, M.; Marignan, J.; Appell, J.; Porte, G.J. Phys. ZZ 1991, 1,1121.
Lamellar to Vesicle Transitions
\
Langmuir, Vol. 9, No. 11, 1993 2049 0=0.015 P
5! X
h
7
d
1
l1 o0 23
10 4
10-3
102
101
0
Q(R1)
Figure 10. Double logarithmic plot of SANS intensity versus scatteringvector Q for sampleof surfactantvolume fraction0.015. Correspondinglight scatteringdata are shown for completeness. Solid line represents the calculated spectra for noninteracting dispersion of lamellae (6 = 25 1A, Ap = 6.5 X 1Olo cm-2).The overlapping SANSdata taken for differentneutron wavelengths and distance from the detector are shown with different symbols.
*
102
1
'"\
\
Figure 13. volume fractions: filled squares,0.015;open trianglea,0.004, fiied triangles, 0.001. The full line represents calculation for bilayers with 6 = 25 A.
P 0.000
10.3
" 102
103
0.4
Q (A') Plot of pI(Q) versus 8 for samples of surfactant
Ck0.025
lol 10.4
0.3
0.2
0.1
1'I; I1
10'
I
0.025
0.050
(A2) Figure 14. ln(Q21(Q)) versus Qafor samplesof surfactantvolume fractions: circles, 0.05; dots, 0.025. Solid line represents linear fit in the intermediate Q range (6 = 26 2 A). Q2
*
Q(A-1)
Figure 11. Double logarithmic plot of SANS intensity versus scatteringvector Q for sampleof surfactantvolume fraction0.025. Correspondinglight scatteringdata are shown for completeness. Solid line represents the calculated spectra for noninteracting dispersion of lamellae (6 = 25 1A, Ap = 6.5 X 1Olo cm-2). 103
C
\
--z 10' -
g
102
-
100
-
I-
z
10-1
lo-'
together with the theoretical curve for bilayers calculated according to eq 3. The best agreement for the position of the maxima in the calculated and experimental curves ia obtained for 6 = 25 f 1 A. The oscillations observed experimentally are damped for the large Q values. It was suggested by Marignan et al.8 that this effect is caused by the fluctuations of the thickness of bilayer. We were able to fit the scattered neutron density using the formula for a statistically isotropic dispersion of large flat particles of constant thicknessm
-
iI io4
IO-^
10-~
io-I
o(A-1) Figure 12. Double logarithmic plot of SANS intensity versus scatteringvector Q for sample of surfactant volume fraction 0.05. Correspondinglight scatteringdata are shown for completeness. Solid line represents the calculated spectra for noninteracting dispersion of lamellae (6 = 25 1 A, Ap = 6.5 X 1O'O cm-% defined interface. Small characteristic dimensions of a scattering objects produce oscillations in the high Q range. Such oscillations are superimposed on the fast asymptotic decrease of the intensity. The patternof these oscillations can be conveniently studied in a plot of @I(Q)versus Q. Figure 13 shows this type of plot for measured samples
*
where is the surfactant volume fraction, 6 is the flat particle thickness, and Ap is the difference between the scattering length density of surfactant and heavy water. The solid curves in Figures 10-12 were fitted using the bilayer thickness 6 = 25 f 1 A and contrast Ap = 6.55 X 1O1O cm-2, whereas the calculated value of the excess scattering length density is Ap = 6.56 X 1O1O cm-2. The agreement is excellent. Another way to obtain the value of bilayer thickness is the fit to the Guinier equations0in the Q range where QS < 1and Q > L - 1, where L is the dimension characteristic of the lateral extension of flat bilayer. The result is shown in Figure 14 and the value of 6 = 26 f 2 A obtained from the slope agrees very well with that obtained above. ~~
(50) Glatter, 0.;Kratky, 0.Small Angle X-ray Scattering; Academic
Press: London, 1982.
Radlihska et al.
2850 Langmuir, Vol. 9, No. 11, 1993
the small amount of residual ions present in the sample. These can be excess ions introduced during ion exchange processes, be monomers of DDAB, be small amounts of single chain surfactants, or originate from the pH of the solution. In a previous study by Dubois31the ionic strength of binary surfactant systems was in the range from 10-4 to le5M. With these values of ionic strength in mind, one can estimate the correlation length close to the La phase boundary. Mitchelland NinhamZ7have shown that for large surface charge, the bending constant k, is given by k, 4eoe k T 2 (4) K
a 4 7
X
-E
0
g3 v,
z
w
n w
=-($)
cc: E1
a 0
v,
0 0.02
0.04
0.06 0.08
0 (A-’)
Figure 15. SANS intensity versus Q for sample containing 10% (w/w)of DDAA (mostly lamellar phase).
The origin of the broad scattering peak at log Q = -1.4 is not obvious. Its position corresponds to a characteristic distance of 140A. This distance cannot be related to the layering of symmetric sponge phase, since it follows from volume balance considerationsthat the statistical distance between the lamellae is 1500 and 720 A for the 0.025and 0.05 samples, respectively. (The corresponding values of Q fall inside the gap between the neutron scattering and light scattering data in Figure 10-12.) Furthermore, the position of this peak does not depend on the volume fraction of surfactant. Therefore, one could speculatethat the distance of 140A is characteristic of some local periodic undulation of single lamellae. The effects of such deformations, thermal undulations,51and structural defects52 have been discussed by other authors. SANS data for sample containing 10% (w/w) DDAA are shown in Figure 15. This is a typical scattering pattern for the lamellar phase. The Bragg peak superimposed on the falling background corresponds to an interlamellar spacing of D = 270 A. Given the bilayer thickness of 25 A this corresponds to a sample containing 99% of the total volume of lamellar phase and 1 % of sponge phase. The background scatteringmay be explained by membrane u n d u l a t i o n ~and/or ~ ~ , ~ ~scattering by the sponge phase regions.” Both SANS and light scattering data clearly indicate existence of a two-phase region between the symmetric L3 and lamellarphase, in agreement with the recent prediction by C a t e of ~ the ~ ~first-order transition between these two phases. However, due to small density contrast and good stability of the spontaneous emulsion, these two phases could not be separated. It has been shown in the case of DDABM that the maximum swelling of the lamellar phase is controlled by (51) Nallet, F.; Roux,D.; Milner, S. T. J.Phys. (Paris) 1990,51,2333. (52)KBkicheff, P.;Cabane, B. J. Phys. Lett. 1984,45, L-813. (53)Porte,G.;Marignan, J.; Bassereau, P.; May, R. Europhys. Lett. 1988, 7, 713. (54)Roux, D.; Safinya, C. R. In Physics of Amphiphilic Layers; Meunier, J., Langevin, D., Boccara, N., Eds.;Springer-Verlag:. Berlin, 1987; p 138. (55) Cates, M. E. Physica A 1991,176, 187.
where e is the dielectric constant of water, e is the charge of electron, and K is the inverse Debye length. According to the general classification given by Higgs and J0anny6~the DDAA case is at the borderline between the Gouy-Chapman region and the intermediate region. Since no analytic prediction of kc exists in the GouyChapman region, we use the expression iven by Mitchell and Ninham with 100 A < K - ~< 1000 , and, therefore, 1 . 5 k ~ T< kc < 15k~Tformaximum swelling of 300 A. For the bilayer in the L3 symmetric state, one expects the persistence length 5k4’ as
1
where a is the size of surfactant molecule. Using eq 5 to calculate the persistence length in the symmetric sponge phase close the lamellar phase boundary, one obtains 3000 A < tk < divergent, which is consistent with the correlation length of 10 000A determined experimentally for the surfactant volume fraction 0.025. ~
4. Conclusions The light scattering, electrical conductivity, and small angle neutron scattering data indicate that the binary DDAA/water system undergoes a series of phase transitions with increased volume fraction of surfactant. In the region 4.4 X 10-6 < 40 I0.002,a dilute vesicular phase existing for very low values of surfactant volume fraction evolves into the asymmetric sponge phase. For some volume fraction in the range 0.0022< q& < 0.005,a second order asymmetric/symmetricspongephase transition takes place. The symmetric sponge phase extends up to & = 0.025. For larger values of ds a mixture of symmetric sponge and lamellar phase is observed,which is indicative of the first-order L$L, phase transition. For d0= 0.1the lamellar phase occupies 99% of the total volume. The sponge phase region is characterized by very large correlation lengths of the order parameter 71. These lengths are at least 2300 A and increase to at least above 16 000 A in the vicinity of critical region. Acknowledgment. We thank K. Fontell for advice on preparing surfactant and S. MarEelja and P. Kbkicheff for stimulating discussions. E.Z.R. acknowledges the hospitality of Groupe Colloide of the Service de Chimie Molbculaire, Centre #Etudes de Saclay. (66)Zemb,T.;Belloni,L.;Dubois,M.; Marcelja,S.Prog. ColloidPolym. Sci. 1992, 89, 33. (57) Higgs, P. G.; Joanny, J.-F. J.Phys. (Paris) 1990,51, 2307.
